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Pi squared is nearly 10

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41–50 of 55 posts

Re: Pi squared is nearly 10

#42
post #37

The second fact, pi^2 ~= g, is famous enough that it has a separate section in Wikipedia [1]. [1] https://en.wikipedia.org/wiki/Mathematical_coincidence#Gravi...

I dislike most of the usual physical “coincidence” examples, because many of them are really the result of human choices: historical conventions, unit definitions, or the order in which things happened to be discovered. They can be explained, and at most there is some interesting scientific history behind them. They are not deep mysteries. The more interesting cases are different. They are unit-independent, or they c…

> Similarly, the ratio between the proton mass and the electron mass is approximately 1836

https://en.wikipedia.org/wiki/Proton-to-electron_mass_ratio says it is

  1836.152673426(32)
So, it differs about 0.153 from its nearest integer. Over 30% of all reals are that close or closer to their nearest integer, so I wouldn’t call that extraordinary at all.

For the fine structure constant, that’s about

  1/137.035999177
Closer, but still not extraordinary. The math is different but I think it’s about a 1:15 chance that a random real will be relatively that close to the reciprocal of an integer.

Re: Pi squared is nearly 10

#43
post #32

Also number of McDonald's in the world divided by number of McDonald's in US is close to pi. Within 1%.

This does not seem to be true currently. In 2025, there were 45356 McDonald's restaurants worldwide and 13706 in the United States, which is about 3.3092.

https://corporate.mcdonalds.com/content/dam/sites/corp/nfl/p...

However, in 2023, the numbers were 41822 / 13457 = 3.1078, which is (almost) within 1 % difference.

https://corporate.mcdonalds.com/content/dam/sites/corp/nfl/p...

Re: Pi squared is nearly 10

#44
post #18

I like the 4-5-6 theorem: pi^4 + pi^5 = e^6 Well, to five decimal places, anyway. Some other good ones: e^pi - pi = 20 sqrt(2) ln pi = phi There are also famous "almost integers" such as this one discovered by Ramanujan: e^(pi sqrt(163)) Which is an integer to 12 decimal places. Edit: I just remembered I have public JupyterLite notebooks for both of these: https://notebooks.oranlooney.com/lab/index.html?path=fake_ma.…

(e^pi - pi)/pi^4 ~= i^i

Re: Pi squared is nearly 10

#46
post #18

I like the 4-5-6 theorem: pi^4 + pi^5 = e^6 Well, to five decimal places, anyway. Some other good ones: e^pi - pi = 20 sqrt(2) ln pi = phi There are also famous "almost integers" such as this one discovered by Ramanujan: e^(pi sqrt(163)) Which is an integer to 12 decimal places. Edit: I just remembered I have public JupyterLite notebooks for both of these: https://notebooks.oranlooney.com/lab/index.html?path=fake_ma.…

the Ramanujan one has some relatively high powered mathematical explanation

https://en.wikipedia.org/wiki/Heegner_number

Re: Pi squared is nearly 10

#47
post #18

I like the 4-5-6 theorem: pi^4 + pi^5 = e^6 Well, to five decimal places, anyway. Some other good ones: e^pi - pi = 20 sqrt(2) ln pi = phi There are also famous "almost integers" such as this one discovered by Ramanujan: e^(pi sqrt(163)) Which is an integer to 12 decimal places. Edit: I just remembered I have public JupyterLite notebooks for both of these: https://notebooks.oranlooney.com/lab/index.html?path=fake_ma.…

> Which is an integer to 12 decimal places this isn't something I was expecting to read today. I guess this works with weak types? /s

That's why the time is Almost instead of just T.

Re: Pi squared is nearly 10

#48
post #18

I like the 4-5-6 theorem: pi^4 + pi^5 = e^6 Well, to five decimal places, anyway. Some other good ones: e^pi - pi = 20 sqrt(2) ln pi = phi There are also famous "almost integers" such as this one discovered by Ramanujan: e^(pi sqrt(163)) Which is an integer to 12 decimal places. Edit: I just remembered I have public JupyterLite notebooks for both of these: https://notebooks.oranlooney.com/lab/index.html?path=fake_ma.…

the Ramanujan one has some relatively high powered mathematical explanation https://en.wikipedia.org/wiki/Heegner_number

Wikipedia also notes that “Ramanjuan’s constant” was actually discovered by Charles Hermite in 1859 and it was a 1975 April Fools article in Scientific American that attributed it to Ramanujan.

Re: Pi squared is nearly 10

#49
post #10

I was a little disappointed that the upper range of gravity on earth only goes to 9.8337. Just a little more and there would have been somewhere on earth that was an exact match. It would have been the ideal (if chilly) place to start a cult.

The initial definition of the meter would have been such that g=pi^2. It was then adjusted but enough for it to remain an interesting (if not too good) approximation.

Re: Pi squared is nearly 10

#50

Earlier quoted context omitted.

the Ramanujan one has some relatively high powered mathematical explanation https://en.wikipedia.org/wiki/Heegner_number

Wikipedia also notes that “Ramanjuan’s constant” was actually discovered by Charles Hermite in 1859 and it was a 1975 April Fools article in Scientific American that attributed it to Ramanujan.

Stigler's Law of Eponymy strikes again!

https://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy

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